Cointegration and causality relationship of Indian stock market with selected world markets

Background: The purpose of this study is to explore the trends and causes of established and emerging nations’ stock market integration with India. The National Stock Exchange (NSE) indices act as a counterweight to international market indices. This study investigates the sustained interest of foreign investors in the Indian stock market in the wake of capital market reforms, as well as whether it moves in tandem with other markets in Asia and the United States. Methods: Our study examined the possibility of cross-country cointegration between the largest economies and indices around the world using multiple financial econometric models, such as Augmented Dickey-Fuller, Unit Root, Correlation, and Johansen Cointegration. Results: The findings of this study significantly support the notion that Indian and international financial markets are highly integrated. Vector error correction model indicates that the Indian market (NSE) is highly cointegrated with the US market (National Association of Securities Dealers Automated Quotations) and increased volatility signifies global contagion. Conclusion: A cursory examination of the data reveals distinct investment and portfolio diversification options for global investors. This could assist regulators in formulating more effective rules regarding price discovery processes.

Any reports and responses or comments on the

Introduction
Global stock market connections have been studied extensively.However, there has not been a great deal of academic interest in examining the interdependence of Emerging stock markets.An economic spillier occurs when one event sets off another event in a similar way, having an impact on economies both within and outside a country.In 2008, when Lehman Brothers collapsed in the U. S., the domino effect hit the economies worldwide including India (Aloui et al., 2016).Financial markets today are closely interconnected and driven by trust.Therefore, the developed and emerging markets have been a riveting field for the research of behavioural finance due to interlinked stock markets across the world.Lai et al. (2016) examined during the crisis, investors make errors of judgment as long as a group of investors takes irrational decisions that lead to worsening the situation of the stock market.
COVID-19 also delivered a shock to the economies of most countries, because of the nature of the interconnected global market (Karkowska and Urjasz, 2021).The Indian stock market has been broadly resilient amidst the COVID-19 crisis so far, despite the devastating waves of the pandemic (Kapoor et al., 2020).However, the Indian economy has witnessed some impact from the global crash.Seth and Panda (2020) discussed that it is hard to pinpoint exactly the impact of any financial crisis on the Indian stock market, but it seems that the COVID-19 crisis has spilled over into some sectors.Numerous studies (Shaikh, 2021; Dhall and Singh, 2020; Singh and Neog, 2020) have argued on insignificant causal linkage of the stock markets across the world.Some authors such as Zhang and Hamori (2021), have also focused on the possible factors and impacts of the global crisis on the Indian market.Hoque et al. (2007) investigated the co-movement of the Bangladesh market with those of Japan, the United States, and India and discovered evidence of a shared stochastic trend.In his paper, it was clear that shocks in the US affected Bangladesh, which is an emerging country.Rajwani and Mukherjee (2013) examined the interconnectedness of the Indian stock market with other Asian stock markets and discovered that the Indian stock market is not interconnected with any of the Asian stock markets, demonstrating the insensitivity of the Indian stock markets to other markets.Several studies have identified both short-term and longterm cointegration and interconnected financial markets between different economies of the world (Stawiarski, 2021; Yarovaya and Lau, 2016).The global financial markets are closely interconnected and driven by the emotions of the investors (Huang et al., 2020).Hence, this manuscript focuses a causal linkage and cointegration between the global crisis and the Indian stock.In previous studies such as Mukherjee and Bose (2008) and Rajwani and Mukherjee (2013), Asian economies have been integrated with the economies of developed nations such as Japan and the United States.
In this study, we contribute to the literature on strategic financial decision-making for investors.Using vector auto regressive correlation (VAR) and vector error correction method (VECM) to assess the cointegration (Yarovaya and Lau, 2016; Kanjilal and Ghosh, 2017; Aggarwal and Raja, 2019), have documented the multivariate cointegration-vector autoregression method and their results indicate that the Indian stock market return depends on the world market returns.This study's main objective is to comprehend how the volatility index of the Indian stock market might be impacted by the volatility index of some other countries.The Indian Capital Market has been examined by various academics at various times for its efficiency and co-integration.Utilizing the Engle-Granger test of co-integration, this study examines the cointegration characteristics of the Indian Capital Market with global markets in the post-liberalization period.Since there are so many markets and so much trade, no amount of research can adequately explain the behaviour.Indian capital markets and other capital markets around the world are investigated in this study.
Accordingly, the article is organized as follows: Section 2 summarizes existing studies that have used cointegration tests on the stock market.Section 3 describes the technique used in the article.Section 4 goes over the data, including possible structural breaks.Section 5 displays the cointegration test findings.Section 6 explores the ramifications of the findings, and Section 6 concludes.

REVISED Amendments from Version 3
We have addressed all comments and made the necessary revisions to ensure the manuscript meets the high standards of your esteemed journal.We are confident that the final version of the manuscript reflects the valuable feedback provided by the reviewers and is now ready for publication.The changes are as follows: 1.The error correction term has been added though the separate table is also provided.
2.The level of the unit root test has been revised.3.The diagnostics have been conducted at the same lag.
4.The study has used the variance decomposition to validates the findings to the extent of cointegration.
Any further responses from the reviewers can be found at the end of the article  (Vo, 2020) studied the significant positive link between foreign investors and crash risk due to the asymmetry of information in the emerging market.Among BRICS (Brazil, Russia, India, China, and South Africa) a diverse responses to the stock market volatility reported including negative and positive shocks (Salisu and Gupta, 2020).Cui and Zhang (2020) have suggested that negative information creates fear among the investor which leads to a larger stock price crash risk.According to Nikkinen and Peltomäki (2020), investors' crash worries are examined by using published newspaper articles and web search volumes.They examine how information supply and demand relate to investor anxiety and their effects on stock market returns, implying that media contribute to the efficiency of information transmission.Long-term cointegration of stock markets was not discovered, but correlation analysis revealed that stock market integration was growing with time.
Even though the majority of the COVID-19 economic crisis has passed, further research is still needed on the developed and rising Asian markets.In addition, it would be interesting to know whether the effect of the crisis on the Indian stock market persists over time and, if so, for how long.Do the recent shocks to global markets alter the standard deviation of forecasting errors in the Indian stock market?Contributing to existing theory and strategic financial decision-making for investors, this paper offers valuable insights.In particular, the authors explore how the global volatility index's shock influences the Indian volatility index, how long the impact lasts, and the degree and sign of the effect.

Methods
In our study, we examined data from several major indices, including the NSE in India, the NIKKEI (Japan's Nikkei 225 Stock Average) in Japan, NASDAQ (National Association of Securities Dealers Automated Quotations), DJI (Dow Jones Industrial Average) and S&P (Standard and Poor index) in the United States, the FTSE (Financial Times Stock Exchange) in the UK, the DAX (Deutscher Aktien Index) in Germany, the FTXIN (FTSE-Xinhua China A50 Index) in China, Cotation Assistée en Continu (CAC) benchmark of France stock market and the Hang Seng in Hong Kong.The descriptive statistics for all indexes' returns are shown in Table 3.We compiled and collected the data from different websites (including Yahoo, Investing.comand NSE India) over the long-term, encompassing a significant portion of the recession from January 1, 2008, to December 2, 2021.The time period covered by the research has been selected to provide an in-depth look at the worldwide correlations that have an effect on the Indian stock market over the long term.
Although the trading hours of each stock exchange varies, the time frame is the exact same for all indexes.Therefore, in order to examine the group statistics, we have taken the common sample.We calculated the daily return by applying the [Return=log (Closing price of indices/Closing price of indices (-1))] equation over the closing price.We analysed the data using the EViews 12 (University Version) software package.The Johansen cointegration test (Menon et al., 2009) 1 is used to demonstrate a long-term link between variables.To determine short-term and long-term associations between variables, the vector error correction model was utilised followed by Ezeibekwe (2021).
Hypothesis H0: There is no long-term linear interdependency between the NSE index and the global index.
H1: There is a long-term linear interdependency between the NSE index and the global index.

Vector error correction model
This model is adopted when variables are cointegrated.VAR indicates the cointegration of the variables over the short term.In addition, by incorporating error correction terms, the model examines the long-term causal relationship (Golder et al., 2020).The number of variables can be measured by using the equations below.The vector autoregressive model of order 1 is called VAR (1): Engle-Granger model is used to measure (Stawiarski, 2021)

Johansen cointegration test
In Johansen cointegration 2 , the number of independent linear combinations (k) that give a stationary process is determined for (m) time series variables.The results are given as cointegration ranks.There is no cointegration relationship when the rank is 0, and there is a cointegration equation when the rank is 1, and so on.Johansen cointegration test analyses the relationship between the NSE index and global index by using Eigen-values and trace statistics.
Integration is based on how many times a series need to be differentiated to produce a stationary series.The Johansen cointegration test is a statistical method used to determine the presence of cointegration among a set of time series variables.Cointegration implies a long-term relationship between these variables, which is essential for various econometric models and time series analysis.In the test, 'P' denotes the number of cointegration vectors (also known as the cointegration rank).It represents the maximum number of linearly independent combinations of the variables that exhibit a stationary behaviour.'m' represents the number of variables in the system being tested, and 'k' is the number of deterministic terms (e.g., intercept or time trend) included in the model.The first difference generates an integrated series known as I (1).As a result, a time series with I (0) is stationary; if I (1), the level is stationary and the change is stationary.The equation below determines cointegration: Null Hypothesis; H0: When k = 0, then p = m, there is no linkage among the variables 3 .
Alternate Hypothesis; H1: 0 < k < m, 0 < p < m There is a significant linkage among the variables.

Descriptive statistical analysis
Individual observations show large shifts during crisis times are further followed by large shifts in the return of the NSE indices and the global indices representing the wild and calm periods of volatility clustering.Figure 1 shows the clustering of the volatility for the daily return of indices, firstly noted by Mandelbrot and Taylor (1967) 'large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes.' Figure 2 represent the leptokurtic statistical distributions with kurtosis greater than three results to a greater extent of volatility because of positive or negative shocks in the stock market.While the Jerque-Bera of NSE daily return (32031.42)measures the high volatility.The shape of the curve and the value of kurtosis along with the low probability value reveal the possibility for   Mukherjee and Bose (2008) posited cointegration, vector auto-regression, vector error-correction models, and Granger causality and found that the U.S. market leads all Asian markets in terms of information.the rejection of the null hypothesis.The skewness measures the asymmetry of a time series over a given period (normal skewness; 0, positive skewness; long right tail, negative skewness; long left tail).
Table 1 indicates that the left-hand tail of the German Blue chip stock market (DAX) is smaller than the right-hand tail.
In other indices, a negative skewness (the left-hand tail is larger than the right-hand tail) indicates a scenario of small wins and few large losses for investors.specify that the huge gain covers the small losses of investors.The Indian stock market exhibits a positive correlation with the world market, as seen in Table 2; however, the correlation of all variables is not strong enough to explain the cointegration.
Table 2 examines the correlation trends between the Indian market and a few selected global markets, indicating that there is a relationship between the Indian stock market and other markets; nevertheless, Figure 3 illustrates that this connection is sometimes parallel to the global economy.
It is said that the "flap of a butterfly's wings in Brazil could set off a tornado in Texas" (Lorenz, 2000) that is not true in the Indian context.The Indian stock market is still linked to the world market because the NSE has a positive correlation with all global indexes, despite the fact that this correlation has been reducing significantly.

Unit root test analysis
A unit root test determines whether a time series is stationary.The null hypothesis defines time series as having a unit root, while the alternative hypothesis defines them as being stationary.Table 3 indicates the value of t statistics in all variables exceeds the critical value.
In this case, these variables were tested again at a difference of one, and the result indicated a null hypothesis, i.e., that the series of all variables are integrated over four lag of order one.To perform Johansen's cointegration test we employed the VAR lag order selection criterion.Table 4 identifies the AIC value at the seventh lag so we examined the cointegration test by using the seventh lag, recommended by AIC.A Japanese statistician (Akaike, 1974) developed the Akaike information criterion.It currently serves as a paradigm for the foundations of statistics and is also commonly employed for statistical inference.The Akaike information criterion (AIC) is an estimator of prediction error and, therefore, relative model quality for a given set of data.Given a set of data models, AIC determines the quality of each model in comparison to the other models.When a statistical model is employed to depict the process that generated the data, the representation is virtually never perfect; as a result, some information is lost.AIC assesses the relative amount of information lost by a particular model; the less information a model loses, the higher the model's quality.

Johansen's cointegration test results
Table 5 shows the statistical values of Johansen's cointegration test.In addition, it provides information about the maximum Eigen-value.Statistics for all variables dependent (NSE) and independent (World's indices) demonstrate a perfect correlation of cointegration.Since the calculated value of statistics and maximum Eigen-values (Table 6) are greater than the critical value (at 5% level) of (MacKinnon et al., 1999), the null hypothesis of no cointegration is rejected in favour of the alternative hypothesis of cointegration.Therefore, the Indian stock market and the global stock market have ten cointegration equations.
We employ VECM to evaluate the short-run characteristics of the cointegrated variables in order to ascertain whether they remain stationary over time (Table 7).If cointegration has been found between series, we are aware that there is a longterm equilibrium link between them.
We estimated nine error correction equations using cointegrated vectors that are negative and highly significant at 1%.This demonstrates the presence of a stable long-run autoregression (Table 7).The coefficient of ECM is -6.92E-06, indicating a causal link across variables.Table 8 shows the error correction for the short term, which is represented by the adjustment coefficient for a percentage change.Furthermore, the data show that the Indian (lag 1), United States (lag 1), United Kingdom, Japan, and Chinese (lag 1 and 2) markets are all impacted by their respective lags.The worldwide market also has a significant impact on the Indian stock market (see Table 9).The equation can be written as- Granger causality test is used to validate the utility of one variable for forecasting another.The outcomes derived from doing the Granger causality test on certain pairs of time series are displayed in Table 10.At a significance level of 5%, It has been determined that the Indian stock market (Nifty 50), China, France, and the United States have a bidirectional causal link, whereas the stock markets of Japan, the United Kingdom, and Germany have a unidirectional causal association.
The effectiveness of market connectivity is measured by residual diagnostics for heteroscedasticity, which aid in identifying heteroscedasticity (Table 11).One can determine whether the model can be trusted based on this.Probability scores over 0.05 indicate that the model should work for the Indian stock market.The effectiveness of market connectivity is measured by residual diagnostics for heteroscedasticity, which aid in identifying heteroscedasticity (Table 11).One can determine whether the model can be trusted based on this.Probability scores over 0.05 indicate that the model should work for the Indian stock market (Table 12).The Jarque-Bera test in statistics determines if sample data have skewness and kurtosis that are consistent with a normal distribution.The result of Table 13 shows that the regression residual is normally distributed since the p value is greater than 0.05.
The null hypothesis is accepted for the sample based on the serial correlation test results, which show that the p-value is greater than 0.05 at the 5% significance level.The serial correlation verifies the accuracy and validity of the results of the cointegration test (Table 14).Serial correlation test findings at lag 4 and 5 indicate that the p-value is less than 0.05 at the 5% significance level, hence rejecting the null hypothesis for the sample.The serial correlation fails to corroborate the accuracy and validity of the cointegration test results (Table 15).Consequently, we transitioned to variance decomposition analysis.
According to the graphical structure (Figure 4), global indices can explain approximately 5-20 percent of India's prediction error variance, whereas India can explain approximately 5-10 percent of the worldwide indices' forecast error.
The Table 16 (extended data; Ali et al., 2024) illustrates the outcomes of VD generated by a multivariate VAR system for both the Indian and global markets.The results of the variance decomposition (VD) analysis in India indicate that it accounts for all of its own forecast error variance for the 1-day ahead prediction, and 95.45 percent of its own forecast error variance for the 10-days ahead forecast.The VD analysis shows that the forecast error variance in India is not significantly influenced by Japan.Conversely, the variance decomposition of Japan accounts for 99.93 percent of its own 1-day prediction error variance and exhibits nearly identical values for the 10-day forecast error variance.Similarly, whether looking at horizons of 1-day and 10-days ahead, NSE accounts for 6.7 and 11.9 percent respectively, of the variance in forecast errors for the Nikkei.
In Figure 5, we show impulse response functions associated with the non-factorized one standard deviation of innovations for the Indian stock market and the stock markets of some of India's top trading partners and developed nations.It depicts the negative impulse responses of the Chinese and Japanese stock markets.Interestingly, both markets are responding similarly to a shock to the Indian stock market in their respective stock markets.Geographic proximity may be the reason for this.The established stock markets of the United States and other economies have a distinct trend.It demonstrates that these markets are in fact developed and have a robust positive impulse reaction to the Indian stock market.

Empirical results
This study shows innovations in the Indian stock market do indeed propagate to India's top trading partner's stock markets in a time-varying manner.In this study, the U.S. stock market appears to be the most influential.The analysis of the ADF statistics (Table 3) confirmed the unit root series for all indices and then we determined lag order using the VAR Lag Order Selection Criteria (Table 4) to carry out causality test.To perform the cointegration test, we selected the AIC, indicating the third lag.Table 5 reveals the critical value is less than trace statistics and Max-Eigen values, which rejects the null hypothesis of no causal links, resulting in cointegration equations among all variables.Panel C (Table 7) predicts

Conclusion
The empirical findings suggest that the selected stock markets have a long-term dynamic.According to our research, the volatility of the US stock market considerably affected the Indian stock market.We performed a vector error correction model test to assess the stationary conditions of the series.This test demonstrated that the sequence is stationary.However, the variables become constant after considering the original difference.Cointegration tests show that the Indian stock market is integrated over time owing to the presence of a cointegration vector.A model of error correction demonstrates conclusively that variables are causal in the long-term.The stock market in India is impacted by those in the United States, Great Britain, Japan, and Germany.In addition, we applied the pairwise Granger causality test, which reveals the lead-lag connection across the markets, to test for short-term causative and informational linkages among diverse pairs of markets.According to our findings, the Indian stock market is neither fully connected nor completely decoupled from the global market.Nonetheless, the amount of integration implies that portfolio diversification can still result in substantial risk reduction and return maximisation in both the short-term and long-term by diversifying their portfolio during a crisis.In recent years, the returns on major US stock indices have dominated the returns for Indian stocks.Similar results show that the bank-dominated financial sectors of the ASEAN five and China are increasingly integrated (Caporale et al., 2021).
The study is prone to various limitations because it relies on secondary sources of data, which have inherent limitations, such as the total number of trading days during the study period for each country were different.So, the sample was adjusted with the help of EViews software.A quick glance at the study highlights clear-cut investment and portfolio diversification opportunities for international investors.This may help regulators formulate better policies concerning price discovery mechanisms.Moreover, it is possible to extend the present study to include global contagion issues between the sample countries.This could be done using high frequency data.Considering the comprehensive revisions of your manuscript, we are confident in changing our previous status from 'approved with reservation' to 'approved'.We appreciate the authors' dedication to improving the work and commend their efforts.Once again, congratulations on your insightful work.

Introduction
The problem statement is insufficiently addressed, and the authors include findings from other studies that would be more appropriately highlighted in the Literature Review section.The researcher should emphasize the novel aspects and contributions to existing knowledge of the study.

Literature Review
Many of the writings cited in this column are highly regarded, although literature published before 2010 is generally considered outdated.The citation style and sentence structure in the text does not adhere to the prescribed standards of citation formatting.For instance, the first paragraph's line 19 reads, "Several studies have identified interconnected financial markets between different economies of the world during the 1996-1997 crisis Yang et al. (2003) by applying (VAR) vector auto-regression".Please perform an extensive review and make any necessary changes.
The researchers do not provide any critical analysis or alternative viewpoints to the current body of work; instead, they simply present the actual findings of previous studies.The current composition would benefit from a better structure by being grouped according to the set of arguments that are being criticized.

Methods
The sample size is enough for the study.However, there are some minor errors, such as incorrect table indications (Table 3 indicates an Augmented Dickey-Fuller test statistic rather than a descriptive statistic -in the methodology section, line 6).The authors should label the symbols to make the narration more understandable.To make the table more organized and consistent, 4 decimal places are advised.

Results
The flow of the results has been stated simply and precisely.Throughout the discussion of the results, however, there was a lack of support from previous investigations.Only four sources are cited in the study to support the conclusion.It is strongly encouraged to include other sources to back up the findings and continue the conversation.

Conclusion
The authors did not specify whether this finding met the objectives and provided a response to the hypothesis.Nonetheless, the authors provided a conclusive summary of the findings in the conclusion.This section contains well-written descriptions of the study's limitations.We confirm that we have read this submission and believe that we have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however we have significant reservations, as outlined above.

Uttam Golder
Assistant Professor of Dept. of Finance and Banking, Jashore University of Science and Technology, Jessore District, Khulna Division, Bangladesh

Review Report on Cointegration and causality relationship of Indian stock market with selected world markets
The researcher has identified an interesting topic related to the Cointegration and causality relationship of Indian stock market with selected world markets.Thanks to the authors for their significant reservations, as outlined above.
The benefits of publishing with F1000Research: Your article is published within days, with no editorial bias • You can publish traditional articles, null/negative results, case reports, data notes and more • The peer review process is transparent and collaborative • Your article is indexed in PubMed after passing peer review • Dedicated customer support at every stage • For pre-submission enquiries, contact research@f1000.com He et al. (2020) have examined the futures markets ability to price discover by margin trading on the stock market.Kumar and Misra (2020) have found widespread evidence of long-term similarity among the NIFTY 50 index and the global market.Naik et al. (2020) used GARCH (Generalized Auto-Regressive Conditional Heteroskedasticity) to calculate stock return error distribution.When time series data are heteroskedastic and volatile, the GARCH model is best.GARCH effectively predicted stock market crises (1995-2019) using State Bank of India and Infosys datasets.Elyasiani et al. (2021) analysed market greed by including the skewness index, which measures investor enthusiasm as opposed to investor fear.Previous studies have mainly exclusively explored the integration of Asian economies with other developed nations such as the United States and Japan during the period from 3 rd January 2011 to 29 th December 2017 in the midst of a global financial crisis.According to the literature, during the COVID-19 crisis, domino effects had both short-term and long-term negative consequences on economies all around the world (Salisu and Gupta, 2020).However, there is a contradiction in the argument made by Aggarwal and Raja (2019); Rajwani and Mukherjee (2013) and Menon et al. (2009).

Figure 2 .
Figure 2. Time series plot of returns to NSE (Source: author's calculations).

Table 1 .
Descriptive statistics (common sample) for daily returns of indices.: author's calculations.

©
2023 Syuhada Baharuddin N et al.This is an open access peer review report distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Nurul Syuhada Baharuddin Faculty of Business and Management, Universiti Teknologi MARA Terengganu, Terengganu, Malaysia Nur Azwani Mohamad Azmin Faculty of Business and Management, Universiti Teknologi MARA, Terengganu, Malaysia Dear Authors, Thank you for the thorough revision of the article.We have reviewed the changes made in response to our previous comments, and we are pleased to see that the authors have addressed all the concerns and suggestions.The revisions have significantly improved the clarity, organization, and overall quality of the article.
the work clearly and accurately presented and does it cite the current literature?Yes Is the study design appropriate and is the work technically sound?Yes Are sufficient details of methods and analysis provided to allow replication by others?Partly If applicable, is the statistical analysis and its interpretation appropriate?Partly Are all the source data underlying the results available to ensure full reproducibility?Yes Are the conclusions drawn adequately supported by the results?Yes Competing Interests: No competing interests were disclosed.

Reviewer Report 22
May 2023 https://doi.org/10.5256/f1000research.135998.r172401© 2023 Golder U.This is an open access peer review report distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
2. Literature review A series of recent studies (Choudhary and Singhal, 2020; Kumar et al., 2021; Sahoo and Kumar, 2021; Kartal et al., 2022) has investigated the cointegration relationship of the stock market amid crisis.Some studies (He et al., 2020; Stawiarski, 2021) have explained the causal linkage of Indian stock market with Asian countries while in some other studies, a number of authors have recognized the comprehensive analysis by applying Generalized Autoregressive Conditional Heteroskedasticity Model (Narasimha and Mushinada, 2020) and found very high volatility index of Indian stock market in comparison to developed countries during the COVID-19 crisis.While recent advances in the field of behavioural finance have highlighted the volatility clustering in the Indian stock market through the use of time series data analysis and predictive analytics.According to Khaing et al. (2020), stock trend extraction results matched genuine price movement.These patterns were retrieved with the news effect curve during the global recession 2008-2009.These criteria include timestamp conversion, identifying the necessary verb, stock reference, and identifying advanced trends.Chen (2021) created the new neural network model to develop the prediction model's concepts.Belciug et al. (2021) evaluated the efficacy of a statistical learning framework using an algorithm based on a competitive/collaborative method for generating a reliable real-time forecast of the next stock market transaction price for a share during upswing of the market.Biswas et al. (2021) reviewed numerous models and approaches used in stock market prediction and focused on their advantages and disadvantages during the crisis.Numerous studies have argued that there is insignificant (Goudarzi and Ramanarayanan, 2011) and significant (Aggarwal and Raja, 2019) causal linkage among the stock markets across the world.Some scholars, such as Jain and Biswal (2016), have also focused on the possible drivers of rupee value decline and the influence of the 2014-2015 global crisis on the Indian stock market.It is well established that the global financial markets are closely interconnected Muthukumaran et al.
(2011)and are driven by the emotions of investors.Several studies have identified interconnected financial markets between different economies of the world during1996-1997 crisis Yang et al. (2003) by applying VAR (vector auto-regression).There is a strong co-movement between developing and mature markets, and studies have found a larger correlation among well-established equities markets(Bekaert and  Harvey, 2003; Carrieri et al., 2007).On the other hand, some early literature implies the existence of diversification benefits by investing in both developed and developing economies due to relatively lower correlations between stock markets of such economies (Bekaert and Harvey, 1995; Foerster and Karolyi, 1999).Different experts have come to different conclusions about how stock markets around the world are related to each other.In addition, the relationship between global stock markets is temporally variable; national and global events can alter the nature and intensity of a relationship over time.Depending on its intensity, the phenomenon could last a short time or last for a very long time.Globalization has changed the relationship between various financial markets worldwide (Can Inci et al., 2011).Ahmad et al. (2005) have investigated only short term linkage whilst no significant linkage was found among the Indian Stock Market (NSE), Japanese (Nikkei) and US equity market (Dow Jones) amid crisis by using Granger-causality test.Menon et al. (2009) found that the Indian stock market did not have any causal linkage with the US and Japanese stock markets during the 2008 crisis period by hypothesizing Engle Granger test of co-integration.Siddiqui (2009) concluded that the Indian stock market is integrated with the global market.Some others studies such as Rajwani and Mukherjee (2013) have argued the Indian stock market is not interconnected with the Asian markets.Narayan et al. (2014) have investigated highly positive time varying bilateral correlations by analysing GARCH-dynamic conditional correlations.Yarovaya and Lau (2016) have concluded the asymmetric causality linkage; their results indicating the coupling and decoupling of the Chinese stock market with the UK stock market.Nayak et al. (2016) applied machine learning algorithms and identified that the historical prices of the stocks are combined with sentiments of the investors.Nandy and Chattopadhyay (2019) have explained the unidirectional action from the world's stock exchange indices

Table 2 .
Correlation matrix for the daily returns of indices.
74ble1provides descriptive statistics on daily returns, highlighting Jarque-Bera standard deviation using the same sample for all indices.The NSE returns over the entire period sample shows a negatively skewed distribution of the sample (Jaque-Bera 33817.66,standarddeviation0.013768, Kurtosis 20.31397).In Japan, the statistical moments of the NIKKEI were Jarque-Bera 5525.19, standard deviation 0.0151, and Kurtosis 10.171).Jarque-Bera values for US Market (NASDAQ; 10447.74,standard deviation 0.014376, and Kurtosis 17.26778), (S&P; 23085.57,standard deviation 0.013164), and (DJI; 33669.34,standard deviation 0.012713, and Kurtosis 20.25097).These all show a similar leptokurtic distribution with negative skewness.It is evident from the descriptive statistics that the significant value probabilities and the Jerque-Bera calculation indicate that the residual distribution of daily returns, like other indices (FTSE) Jarque-Bera 13203.88,standard deviation 0.012250 with Kurtosis value 13.81124), Germany (DAX) Jarque-Bera 9850.239, standard deviation 0.014335 with Kurtosis value 12.34726), Hong Kong (HANG SENG) Jarque-Bera 11642.69,standard deviation 0.0126 and Kurtosis 19.89 and France (CAC) Jarque-Bera 8553.046.The values of skewness' and kurtosis observed the volatility clustering and specify the distribution of all indices (variables) is leptokurtic.Only Germany (DAX) is positively skewed, which

Table 4 .
VAR Lag order selection criteria.
LR: sequential; modified LR test statistic, FPE: Final prediction error; AIC: Akaike information criterion; SC: Schwarz information criterion; HQ: Hannan-Quinn information criterion.*Indicates lag order selected by the criterion (each test at 5% level).

Table 7 .
Error Correction Term-Long run cointegration equation.

Table 8 .
Error Correction Term-Short run coefficient.

Table 11 .
VEC Residual Heteroskedasticity Tests (Levels and Squares) Joint test.

Table 12 .
Individual component of Heteroskedasticity Tests.
*Approximate p-values do not account for coefficient.

Table 14 .
Serial Correlation Test at lag h the long-term cointegration equation for the Indian stock market, which suggests that Japan (NIKKEI), US (NASDAQ, DJI, UK (FTSE), Germany (DAX), Hong Kong (HANG SENG) and France (CAC) indices have a positive correlation with Indian Indices (NSE), while China (RFTXIN) and US (S&P) indices have a negative correlation, considering ceteris paribus on Indian stock market.AsSonget al. (2021) have documented supporting evidence, our findings are consistent with the idea that global financial crises have positively influenced interdependence of stock markets in Asian countries.Based on the coefficients, the linkage between the Indian stock market and the global market is statistically significant at a 1% level.Additionally, the Chinese stock market indices and S&P show a negative impact on Indian stock markets and the NASDAQ and Dow Jones indices in the US, Hong Kong (HANG SENG), and Japan (NIKKEI) have shown the strongest long-term correlation with Indian markets.The impulse reaction of NIKKEI to unit shock in NSE causes a little decrease in NSE on days 3 and 4, but an increase on day 6.Between days 8 and 10, this effect increases marginally.Similarly, when a unit shock is applied to NSE, NIKKEI displays a mixed reaction.This is evidence that the Japanese and Indian stock markets are not fully integrated.The impulse response of S&P to a unit shock on the NSE demonstrates that it has a negative impact on the SENSEX on the second day and a positive impact on the third day.It indicates that the NSE is highly cointegrated with the S&P and in the same way, DJI, NASDAQ, FTSE, and CAC.In addition, HNGSNG, DAX, and FTXIN do not have a significant impact on the Indian stock market.Similarfindings are reported by Choudhary and Singhal (2020) and Mukherjee and Bose (2008).In addition, we find that our findings are in line with those ofTripathiand Sethi (2012), Hoque et al. (2007), etc.The correlation results are consistent with Seth and Panda (2020) indicated that the Indian stock market index has a strong positive correlation with the US stock market index.

have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above. Version 2
Figshare: Cointegration and Causality Relationship, https://doi.org/10.6084/m9.figshare.20263803.v2(Ali et al., 2022).Cointegration and causality relationship of Indian stock market with selected world markets" Table 16 Variance Decomposition of RNSE, https://doi.org/10.6084/m9.figshare.26373988.v1(Ali et al., 2024).Data are available under the terms of the Creative Commons Attribution 4.0 International license (CC-BY 4.0). 1.I did not find any error correction term.2. Unit root test results are shown only on 1st difference.The level is not reported.So, it is not possible to understand whether the VECM model is applicable or not.